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-rw-r--r--spartan/core/Spartan.thy72
-rw-r--r--spartan/core/eqsubst.ML4
-rw-r--r--spartan/core/types.ML57
3 files changed, 88 insertions, 45 deletions
diff --git a/spartan/core/Spartan.thy b/spartan/core/Spartan.thy
index 10caa30..6b2ed58 100644
--- a/spartan/core/Spartan.thy
+++ b/spartan/core/Spartan.thy
@@ -181,18 +181,16 @@ axiomatization where
\<rbrakk> \<Longrightarrow> \<Sum>x: A. B x \<equiv> \<Sum>x: A. B' x"
-section \<open>Infrastructure\<close>
+section \<open>Type checking & inference\<close>
ML_file \<open>lib.ML\<close>
ML_file \<open>context_facts.ML\<close>
ML_file \<open>context_tactical.ML\<close>
-subsection \<open>Type-checking/inference\<close>
-
-\<comment> \<open>Rule attributes for the type-checker\<close>
+\<comment> \<open>Rule attributes for the typechecker\<close>
named_theorems form and intr and comp
-\<comment> \<open>Defines elimination automation and the `elim` attribute\<close>
+\<comment> \<open>Elimination/induction automation and the `elim` attribute\<close>
ML_file \<open>elimination.ML\<close>
lemmas
@@ -203,7 +201,20 @@ lemmas
[comp] = beta Sig_comp and
[cong] = Pi_cong lam_cong Sig_cong
-\<comment> \<open>Type-checking\<close>
+\<comment> \<open>Subsumption rule\<close>
+lemma sub:
+ assumes "a: A" "A \<equiv> A'"
+ shows "a: A'"
+ using assms by simp
+
+\<comment> \<open>Basic substitution of definitional equalities\<close>
+ML_file \<open>~~/src/Tools/misc_legacy.ML\<close>
+ML_file \<open>~~/src/Tools/IsaPlanner/isand.ML\<close>
+ML_file \<open>~~/src/Tools/IsaPlanner/rw_inst.ML\<close>
+ML_file \<open>~~/src/Tools/IsaPlanner/zipper.ML\<close>
+ML_file \<open>~~/src/Tools/eqsubst.ML\<close>
+
+\<comment> \<open>Term normalization, type checking & inference\<close>
ML_file \<open>types.ML\<close>
method_setup typechk =
@@ -214,14 +225,26 @@ method_setup known =
\<open>Scan.succeed (K (CONTEXT_METHOD (
CHEADGOAL o Types.known_ctac)))\<close>
-subsection \<open>Statement commands\<close>
+setup \<open>
+let val typechk = fn ctxt =>
+ NO_CONTEXT_TACTIC ctxt o Types.check_infer
+ (Simplifier.prems_of ctxt @ Context_Facts.known ctxt)
+in
+ map_theory_simpset (fn ctxt => ctxt
+ addSolver (mk_solver "" typechk))
+end
+\<close>
+
+
+section \<open>Statements and goals\<close>
ML_file \<open>focus.ML\<close>
ML_file \<open>elaboration.ML\<close>
ML_file \<open>elaborated_statement.ML\<close>
ML_file \<open>goals.ML\<close>
-subsection \<open>Proof methods\<close>
+
+section \<open>Proof methods\<close>
named_theorems intro \<comment> \<open>Logical introduction rules\<close>
@@ -270,6 +293,7 @@ subsection \<open>Reflexivity\<close>
named_theorems refl
method refl = (rule refl)
+
subsection \<open>Trivial proofs (modulo automatic discharge of side conditions)\<close>
method_setup this =
@@ -278,16 +302,9 @@ method_setup this =
(CONTEXT_TACTIC' (fn ctxt => resolve_tac ctxt facts))
facts))))\<close>
-subsection \<open>Rewriting\<close>
-\<comment> \<open>\<open>subst\<close> method\<close>
-ML_file \<open>~~/src/Tools/misc_legacy.ML\<close>
-ML_file \<open>~~/src/Tools/IsaPlanner/isand.ML\<close>
-ML_file \<open>~~/src/Tools/IsaPlanner/rw_inst.ML\<close>
-ML_file \<open>~~/src/Tools/IsaPlanner/zipper.ML\<close>
-ML_file \<open>eqsubst.ML\<close>
+subsection \<open>Rewriting\<close>
-\<comment> \<open>\<open>rewrite\<close> method\<close>
consts rewrite_HOLE :: "'a::{}" ("\<hole>")
lemma eta_expand:
@@ -315,20 +332,18 @@ ML_file \<open>~~/src/HOL/Library/cconv.ML\<close>
ML_file \<open>rewrite.ML\<close>
\<comment> \<open>\<open>reduce\<close> computes terms via judgmental equalities\<close>
-setup \<open>map_theory_simpset (fn ctxt =>
- ctxt addSolver (mk_solver "" (fn ctxt' =>
- NO_CONTEXT_TACTIC ctxt' o Types.check_infer (Simplifier.prems_of ctxt'))))\<close>
-
method reduce uses add =
- changed \<open>repeat_new \<open>(simp add: comp add | sub comp); typechk?\<close>\<close>
+ changed \<open>repeat_new \<open>(simp add: comp add | subst comp); typechk?\<close>\<close>
-subsection \<open>Congruence automation\<close>
+
+subsection \<open>Congruence relations\<close>
consts "rhs" :: \<open>'a\<close> ("..")
ML_file \<open>congruence.ML\<close>
-subsection \<open>Implicits\<close>
+
+section \<open>Implicits\<close>
text \<open>
\<open>?\<close> is used to mark implicit arguments in definitions, while \<open>{}\<close> is expanded
@@ -364,7 +379,8 @@ translations
translations "\<lambda>x. b" \<leftharpoondown> "\<lambda>x: A. b"
-subsection \<open>Lambda coercion\<close>
+
+section \<open>Lambda coercion\<close>
\<comment> \<open>Coerce object lambdas to meta-lambdas\<close>
abbreviation (input) lambda :: \<open>o \<Rightarrow> o \<Rightarrow> o\<close>
@@ -389,7 +405,7 @@ Lemma refine_codomain:
"f: \<Prod>x: A. B x"
"\<And>x. x: A \<Longrightarrow> f `x: C x"
shows "f: \<Prod>x: A. C x"
- by (subst eta_exp)
+ by (rewrite eta_exp)
Lemma lift_universe_codomain:
assumes "A: U i" "f: A \<rightarrow> U j"
@@ -463,12 +479,12 @@ lemma
Lemma id_left [comp]:
assumes "A: U i" "B: U i" "f: A \<rightarrow> B"
shows "(id B) \<circ>\<^bsub>A\<^esub> f \<equiv> f"
- by (subst eta_exp[of f]) (reduce, rule eta)
+ by (rewrite eta_exp[of f]) (reduce, rule eta)
Lemma id_right [comp]:
assumes "A: U i" "B: U i" "f: A \<rightarrow> B"
shows "f \<circ>\<^bsub>A\<^esub> (id A) \<equiv> f"
- by (subst eta_exp[of f]) (reduce, rule eta)
+ by (rewrite eta_exp[of f]) (reduce, rule eta)
lemma id_U [type]:
"id (U i): U i \<rightarrow> U i"
@@ -494,7 +510,7 @@ Lemma fst_comp [comp]:
Lemma snd_type [type]:
assumes "A: U i" "\<And>x. x: A \<Longrightarrow> B x: U i"
shows "snd A B: \<Prod>p: \<Sum>x: A. B x. B (fst A B p)"
- unfolding snd_def by typechk reduce
+ unfolding snd_def by typechk
Lemma snd_comp [comp]:
assumes "A: U i" "\<And>x. x: A \<Longrightarrow> B x: U i" "a: A" "b: B a"
diff --git a/spartan/core/eqsubst.ML b/spartan/core/eqsubst.ML
index 31d5126..5ae8c73 100644
--- a/spartan/core/eqsubst.ML
+++ b/spartan/core/eqsubst.ML
@@ -430,12 +430,12 @@ val _ =
Method.setup \<^binding>\<open>sub\<close>
(parser >> (fn ((asm, occs), inthms) => fn ctxt => SIMPLE_METHOD' (
(if asm then eqsubst_asm_tac else eqsubst_tac) ctxt occs inthms)))
- "single-step substitution" #>
+ "single-step substitution" (* #>
Method.setup \<^binding>\<open>subst\<close>
(parser >> (fn ((asm, occs), inthms) => K (CONTEXT_METHOD (
CHEADGOAL o SIDE_CONDS 0
((if asm then eqsubst_asm_ctac else eqsubst_ctac) occs inthms)))))
- "single-step substitution with automatic discharge of side conditions"
+ "single-step substitution with automatic discharge of side conditions" *)
)
end
diff --git a/spartan/core/types.ML b/spartan/core/types.ML
index 70e5057..67918b9 100644
--- a/spartan/core/types.ML
+++ b/spartan/core/types.ML
@@ -43,42 +43,69 @@ fun known_ctac facts = CONTEXT_SUBGOAL (fn (goal, i) => fn (ctxt, st) =>
if Lib.no_vars concl orelse
(Lib.is_typing concl andalso Lib.no_vars (Lib.term_of_typing concl))
then
- let val ths = known ctxt @ map (Simplifier.norm_hhf ctxt) facts
+ let val ths = known ctxt @ facts
in st |>
(assume_tac ctxt ORELSE' resolve_tac ctxt ths THEN_ALL_NEW K no_tac) i
end
else Seq.empty
end)
-(*Simple bidirectional typing tactic, with some nondeterminism from backtracking
- search over input facts. The current implementation does not perform any
- normalization.*)
+(*Simple bidirectional typing tactic with some backtracking search over input
+ facts.*)
fun check_infer_step facts i (ctxt, st) =
let
- val tac = SUBGOAL (fn (goal, i) =>
+ val refine_tac = SUBGOAL (fn (goal, i) =>
if Lib.rigid_typing_concl goal
then
- let val net = Tactic.build_net (
- map (Simplifier.norm_hhf ctxt) facts
- @(cond ctxt)
- @(Named_Theorems.get ctxt \<^named_theorems>\<open>form\<close>)
- @(Named_Theorems.get ctxt \<^named_theorems>\<open>intr\<close>)
- @(map #1 (Elim.rules ctxt)))
- in (resolve_from_net_tac ctxt net) i end
+ let
+ val net = Tactic.build_net (
+ map (Simplifier.norm_hhf ctxt) facts
+ @(cond ctxt)
+ @(Named_Theorems.get ctxt \<^named_theorems>\<open>form\<close>)
+ @(Named_Theorems.get ctxt \<^named_theorems>\<open>intr\<close>)
+ @(map #1 (Elim.rules ctxt)))
+ in resolve_from_net_tac ctxt net i end
else no_tac)
+ val sub_tac = SUBGOAL (fn (goal, i) =>
+ let val concl = Logic.strip_assums_concl goal in
+ if Lib.is_typing concl
+ andalso Lib.is_rigid (Lib.term_of_typing concl)
+ andalso Lib.no_vars (Lib.type_of_typing concl)
+ then
+ (resolve_tac ctxt @{thms sub}
+ THEN' SUBGOAL (fn (_, i) =>
+ NO_CONTEXT_TACTIC ctxt (check_infer facts i))
+ THEN' compute_tac ctxt facts
+ THEN_ALL_NEW K no_tac) i
+ else no_tac end)
+
val ctxt' = ctxt (*TODO: Use this to store already-derived typing judgments*)
in
- TACTIC_CONTEXT ctxt' (tac i st)
+ TACTIC_CONTEXT ctxt' (
+ (NO_CONTEXT_TACTIC ctxt' o known_ctac facts
+ ORELSE' refine_tac
+ ORELSE' sub_tac) i st)
end
-fun check_infer facts i (cst as (_, st)) =
+and check_infer facts i (cst as (_, st)) =
let
- val ctac = known_ctac facts CORELSE' check_infer_step facts
+ val ctac = check_infer_step facts
in
cst |> (ctac i CTHEN
CREPEAT_IN_RANGE i (Thm.nprems_of st - i) (CTRY o CREPEAT_ALL_NEW_FWD ctac))
end
+and compute_tac ctxt facts =
+ let
+ val comps = Named_Theorems.get ctxt \<^named_theorems>\<open>comp\<close>
+ val ctxt' = ctxt addsimps comps
+ in
+ SUBGOAL (fn (_, i) =>
+ ((CHANGED o asm_simp_tac ctxt' ORELSE' EqSubst.eqsubst_tac ctxt [0] comps)
+ THEN_ALL_NEW SUBGOAL (fn (_, i) =>
+ NO_CONTEXT_TACTIC ctxt (check_infer facts i))) i)
+ end
+
end
generated by cgit v1.2.3 (git 2.25.1) at 2025-01-07 05:17:47 +0000